Subgroups — #44397934

Order 29056.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28408858	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₂₂₇	C₂	1	1	yes	maximal, characteristic
3	#20300222	—	2	2	no	—
4	C₂×C₁₆×C₂₂₇	C₂²	1	1	yes	characteristic
5	C₃₂×C₂₂₇	C₄	1	2	yes	complemented
6	C₄⋊Dic₂₂₇	—	4	2	no	—
7	C₂×C₈×C₂₂₇	D₄	1	1	yes	characteristic
8	C₁₆×C₂₂₇	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₂₂₇	Q₈	1	1	yes	characteristic
10	C₂×Dic₂₂₇	—	8	2	no	—
11	C₂×C₄×C₂₂₇	D₈	1	1	yes	characteristic
12	C₈×C₂₂₇	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₂₂₇	Q₁₆	1	1	yes	characteristic
14	C₂²×C₂₂₇	D₁₆	1	1	yes	characteristic
15	C₄×C₂₂₇	#107	1	1	yes	characteristic
16	C₄×C₂₂₇	Q₃₂	1	1	yes	characteristic
17	Dic₂₂₇	—	16	2	no	—
18	C₂×C₂₂₇	#366	1	1	yes	characteristic
19	C₂×C₂₂₇	D₃₂	1	1	yes	characteristic
20	C₂×C₂₂₇	Q₆₄	1	1	yes	characteristic
21	C₂₂₇	#1423	1	1	yes	characteristic, complemented, Sylow
22	#1423	—	227	1	no	maximal, Sylow
23	C₂×C₃₂	D₂₂₇	1	1	yes	characteristic
24	#366	—	227	2	no	—
25	C₂×C₁₆	C₂×D₂₂₇	1	1	yes	characteristic
26	#107	—	454	2	no	—
27	C₃₂	Dic₂₂₇	1	2	yes	complemented
28	C₂×C₈	D₉₀₈	1	1	yes	characteristic
29	C₄⋊C₄	—	908	2	no	—
30	C₁₆	C₂×Dic₂₂₇	1	1	yes	characteristic
31	C₁₆	Dic₄₅₄	1	1	yes	characteristic
32	C₂×C₄	—	1816	2	no	—
33	C₂×C₄	D₁₈₁₆	1	1	yes	characteristic
34	C₈	C₄⋊Dic₂₂₇	1	1	yes	characteristic
35	C₈	Dic₉₀₈	1	1	yes	characteristic
36	C₂²	D₃₆₃₂	1	1	yes	characteristic
37	C₄	—	3632	2	no	—
38	C₄	#20300222	1	1	yes	characteristic
39	C₄	Dic₁₈₁₆	1	1	yes	characteristic
40	C₂	#28408858	1	1	yes	characteristic
41	C₂	D₇₂₆₄	1	1	yes	characteristic
42	C₂	Dic₃₆₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₆₃₂
commutator	C₁₆×C₂₂₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₂₇
Fitting	C₂×C₃₂×C₂₂₇	C₂
socle, prime radical	C₂²×C₂₂₇	D₁₆
cosocle	C₂×C₁₆×C₂₂₇	C₂²
hypercenter	C₂×C₃₂	D₂₂₇
hypocenter	C₂₂₇	#1423
LCS	G ▷ C₁₆×C₂₂₇ ▷ C₈×C₂₂₇ ▷ C₄×C₂₂₇ ▷ C₂×C₂₂₇ ▷ C₂₂₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. C₃₂×C₂₂₇	C₄	semidirect
21. C₂₂₇	#1423	semidirect
27. C₃₂	Dic₂₂₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#28408858	2
C₂×C₃₂×C₂₂₇	2
#1423	227